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These two characters are more similar to each other than either of them are to Ash.
>spent their youth learning about Pokemon
>began their journeys thinking they knew best
>both caught dozens upon dozens of Pokemon in no time
>competitive, but more focused on research and knowledge
Where they differ is that Gary is overly antagonistic, and Goh is way too easily offended by any perceived slight. Both come from a place of pride, but can be pretty bad when they come together. While Goh blew it against Articuno, Gary didn't help by antagonizing one of his partners, knowing full-well how much that'd throw him off.
But I think Gary was less interested in defeating Articuno (knowing his extreme lead in tokens, it probably made no difference to him) than he was in teaching Goh that pride goeth before the fall.
It's been a well executed rivalry, marred only by the pitiful amount of episodes it was featured in. Gary looks, sounds, and is written great. I'd have much preferred double the amount of episodes furthering their dynamic over the seven-or-eight episodes we've spent having Koharu gawk at Eeveelutions before learning nothing and going home.